1. Field of the Invention
The present invention relates to an electromagnetic field simulator which simulates an electromagnetic field and an electromagnetic field simulation program storage medium which stores an electromagnetic field simulation program which causes a computer to simulate the electromagnetic field.
2. Description of the Related Art
An electromagnetic field simulator and electromagnetic field simulation program targeted for communication radio waves are conventionally known, which simulate an electromagnetic field to analyze performance of communication antennas. Furthermore, as a representative technique for simulating an electromagnetic field using such an electromagnetic field simulator and electromagnetic field simulation program, a Finite Difference Time Domain (FDTD) method is known (see, for example, Yee, K. S., “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media”, IEEE Transa, Antennas Propagat., Vol. Ap-14, p. 302-307, 1966, and Toru Uno, “Electromagnetic Field and Antenna Analysis using FDTD Method”, 1998, CORONA PUBLISHING CO., LTD.). This technique spatially and temporally differentiates the Maxwell's equation which is a basic equation describing a time variation of an electromagnetic field and keeps track of the time variation of the electromagnetic field. According to this technique, spacing between grids (steps) used for discretization of space and time is set to a sufficiently small value and a time variation in the electromagnetic field can be simulated in detail. Advantages of such an FDTD method include simplicity of calculation principles, ease of speed enhancement of calculation, ability to evaluate a transient electromagnetic characteristic because a time waveform is calculated in principle and ease of three-dimensional calculation.
A formula whereby a time variation of an electromagnetic field component is calculated using the FDTD method will be shown below. (Excerpt from Allen Taflove, Susan C. Hagness: “Computational Electrodynamics”)
                    [                  Formula          ⁢                                          ⁢          1          ⁢                      -                    ⁢          1                ]                                                                                  E            x                    ⁢                      |                                          i                +                                  1                  /                  2                                            ,              j              ,              k                                      n              +                              1                /                2                                                    =                                            (                                                1                  -                                                                                    σ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                    ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                                                                          ⁢                                              ɛ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                                                                                      1                  +                                                                                    σ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                    ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                              ɛ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                                                                                )                        ⁢                                                  ⁢                          E              x                                ⁢                      |                                          i                +                                  1                  /                  2                                            ,              j              ,              k                                      n              -                              1                /                2                                              ⁢                                    +                              (                                                                            Δ                      ⁢                                                                                          ⁢                      t                                                              ɛ                                                                        i                          +                                                      1                            /                            2                                                                          ,                        j                        ,                        k                                                                                                  1                    +                                                                                            σ                                                                                    i                              +                                                              1                                /                                2                                                                                      ,                            j                            ,                            k                                                                          ⁢                        Δ                        ⁢                                                                                                  ⁢                        t                                                                    2                        ⁢                                                                                                  ⁢                                                  ɛ                                                                                    i                              +                                                              1                                /                                2                                                                                      ,                            j                            ,                            k                                                                                                                                              )                                      ·                          (                                                                                                                  H                        z                                            ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                                                      j                            +                                                          1                              /                              2                                                                                ,                          k                                                n                                            ⁢                                              -                                                  H                          z                                                                    ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                                                      j                            -                                                          1                              /                              2                                                                                ,                          k                                                n                                                                                    Δ                      ⁢                                                                                          ⁢                      y                                                        -                                                                                    H                        y                                            ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                                                      k                            +                                                          1                              /                              2                                                                                                      n                                            ⁢                                              -                                                  H                          y                                                                    ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                                                      k                            -                                                          1                              /                              2                                                                                                      n                                                                                    Δ                      ⁢                                                                                          ⁢                      z                                                        -                                      J                                          source                      x                                                                      ⁢                                  |                                                            i                      +                                              1                        /                        2                                                              ,                    j                    ,                    k                                    n                                            )                                                          (        1        )                                [                  Formula          ⁢                                          ⁢          1          ⁢                      -                    ⁢          2                ]                                                                                  H            x                    ⁢                      |                          i              ,                              j                +                                  1                  /                  2                                            ,                              k                +                                  1                  /                  2                                                                    n              +              1                                      =                                            (                                                1                  -                                                                                    σ                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                                                      k                            +                                                          1                              /                              2                                                                                                      *                                            ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                                                                          ⁢                                              μ                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                                                      k                            +                                                          1                              /                              2                                                                                                                                                                                            1                  +                                                                                    σ                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                                                      k                            +                                                          1                              /                              2                                                                                                      *                                            ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                              μ                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                                                      k                            +                                                          1                              /                              2                                                                                                                                                                                      )                        ⁢                                                  ⁢                          H              x                                ⁢                      |                          i              ,                              j                +                                  1                  /                  2                                            ,                              k                +                                  1                  /                  2                                                      n                    ⁢                                    +                              (                                                                            Δ                      ⁢                                                                                          ⁢                      t                                                              μ                                              i                        ,                                                  j                          +                                                      1                            /                            2                                                                          ,                                                  k                          +                                                      1                            /                            2                                                                                                                                                    1                    +                                                                                            σ                                                      i                            ,                                                          j                              +                                                              1                                /                                2                                                                                      ,                                                          k                              +                                                              1                                /                                2                                                                                                              *                                                ⁢                        Δ                        ⁢                                                                                                  ⁢                        t                                                                    2                        ⁢                                                                                                  ⁢                                                  μ                                                      i                            ,                                                          j                              +                                                              1                                /                                2                                                                                      ,                                                          k                              +                                                              1                                /                                2                                                                                                                                                                                                        )                                      ·                          (                                                                                                                  E                        y                                            ⁢                                              |                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                                                      k                            +                            1                                                                                                    n                          +                                                      1                            /                            2                                                                                              ⁢                                              -                                                  E                          y                                                                    ⁢                                              |                                                  i                          ,                                                      j                            +                                                          1                              /                              2                                                                                ,                          k                                                                          n                          +                                                      1                            /                            2                                                                                                                                      Δ                      ⁢                                                                                          ⁢                      z                                                        -                                                                                    E                        z                                            ⁢                                              |                                                  i                          ,                                                      j                            +                            1                                                    ,                                                      k                            +                                                          1                              /                              2                                                                                                                                n                          +                                                      1                            /                            2                                                                                              ⁢                                              -                                                  E                          z                                                                    ⁢                                              |                                                  i                          ,                          j                          ,                                                      k                            +                                                          1                              /                              2                                                                                                                                n                          +                                                      1                            /                            2                                                                                                                                      Δ                      ⁢                                                                                          ⁢                      y                                                        -                                      M                                          source                      x                                                                      ⁢                                  |                                      i                    ,                                          j                      +                                              1                        /                        2                                                              ,                                          k                      +                                              1                        /                        2                                                                                                  n                    +                                          1                      /                      2                                                                                  )                                                          (        2        )            
Ex, Ey, Ez: Components of electric field
Hx, Hy, Hz: Components of magnetic field
Jsource x: Current source
Msource x: Magnetic current source
∈: Dielectric constant
σ: Conductivity
σ*: Magnetic conductivity
Δx, Δy, Δz: Space grid width
Δt: Time division width
The subscripts i, j, k added at the bottom right of the electromagnetic field components denote space grid numbers and indicate coordinates of a simulation space. Furthermore, the subscripts n, n+1 added to the electromagnetic field components denote numbers indicating time steps and time advances by Δt when a time step advances by 1.
In order to obtain sufficient calculation accuracy using the FDTD method which is a method of calculating a difference formula, a time step and space step in simulation are preferably set to a small value, approximately 1/10 to 1/20 of the period and wavelength of light. Furthermore, in an actual simulation, instantaneous values of X, Y, Z components of the electric field and magnetic field for each grid of a model to be analyzed need to be saved in a main storage device made up of a RAM or the like. Since there is a limitation to the storage capacity of a computer, the size of a model is generally limited to several times the wavelength of an electromagnetic wave.
Since light is an electromagnetic wave having a wavelength of 1 micron or below, the domain that can be calculated using the FDTD method is limited to several microns and there have been only a few cases where the FDTD method is used for light simulations, but techniques for accessing information on an information storage medium using light have been developed in recent years and as near-field optics using optical elements having a structure smaller than the light wavelength become a focus of attention. Thus, there are an increasing number of cases where the behavior of light in a micro domain on the order of several times the light wavelength is analyzed. However, since such near-field optics have large effects of diffraction and cannot handle light as light rays, it is effective to analyze light as an electromagnetic wave using an electromagnetic field simulator and electromagnetic field simulation program using the FDTD method. Accordingly, these days, research into near-field optics applying the FDTD method to an optical model and development and design of optical elements are being actively conducted.
In both simulation of a communication radio wave and simulation of light, it is necessary to set a source for the electromagnetic wave. In the case of the communication radio wave or the like, a current flowing through an antenna or circuit can be set as the source. That is, a desired simulation can be realized by substituting the current of the circuit or the like into current source Jsource x of Formula (1) and Formula (2) and setting magnetic current source Msource x to “0”.
On the other hand, when optical problems are calculated using the FDTD method, light is often introduced from the outside of an analysis domain (simulation space), and so a method of subjecting the electric field to forced vibration at a frequency of the incident wave in part of the simulation space is used to reproduce the incident light. The part where the electric field is subjected to forced vibration is called a “wave source”. This wave source does not exist in an actual analysis target and is virtually set to conduct an analysis.
The simplest scheme for realizing this is to subject the electric field Ex to forced vibration according to Formula (a) shown below without applying Formula (1) to the portion of the wave source:
[Formula 2]Ex|i+1/2,j,kn+1/2=E0|i+1/2,j,k sin(ωt+φ)  (a)
Furthermore, for parts other than the wave source, executing the calculations of Formula (1) and Formula (2) with both the current source Jsource x and magnetic current source Msource x set to “0” causes the vibration of the electric field Ex of the wave source portion to transmit to the electric field and magnetic field within the simulation space and causes light propagation to be simulated. However, subjecting the electric field Ex to forced vibration in this way produces a phenomenon that light is reflected due to the placement of the wave source.
FIG. 1 shows a simulation example based on the scheme under which the electric field Ex is subjected to forced vibration.
This figure shows a model in which a linear wave source 1 is disposed at the top and a reflecting surface 2 is disposed at a position facing the wave source 1. Furthermore, in this model, the wave source 1 is given a current source corresponding to a spherical wave which converges toward the reflecting surface 2.
The simulation result shown in FIG. 1 shows interference patterns parallel to the reflecting surface 2 between the wave source 1 and reflecting surface 2. This is attributable to the fact that light reflected on the reflecting surface 2 is returned to the wave source 1 and further reflected on the wave source 1, causing multiple reflections, which is a wrong result of the presence of the virtual wave source 1 affecting the calculation.
A technique for avoiding such reflection by the wave source 1 is already known and there is a proposal to use Formula (3) instead of Formula (a) above.
                    [                  Formula          ⁢                                          ⁢          3                ]                                                                                  E            x                    ⁢                      |                                          i                +                                  1                  /                  2                                            ,              j              ,              k                                      n              +                              1                /                2                                                    =                                            (                                                1                  -                                                                                    σ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                    ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                                                                          ⁢                                              ɛ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                                                                                      1                  +                                                                                    σ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                    ⁢                      Δ                      ⁢                                                                                          ⁢                      t                                                              2                      ⁢                                              ɛ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                                                                                )                        ⁢                                                  ⁢                          E              x                                ⁢                      |                                          i                +                                  1                  /                  2                                            ,              j              ,              k                                      n              -                              1                /                2                                              ⁢                                                    +                                  (                                                                                    Δ                        ⁢                                                                                                  ⁢                        t                                                                    ɛ                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                          k                                                                                                            1                      +                                                                                                    σ                                                                                          i                                +                                                                  1                                  /                                  2                                                                                            ,                              j                              ,                              k                                                                                ⁢                          Δ                          ⁢                                                                                                          ⁢                          t                                                                          2                          ⁢                                                                                                          ⁢                                                      ɛ                                                                                          i                                +                                                                  1                                  /                                  2                                                                                            ,                              j                              ,                              k                                                                                                                                                            )                                            ·                              (                                                                                                    H                        z                                            ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                                                      j                            +                                                          1                              /                              2                                                                                ,                          k                                                n                                            ⁢                                              -                                                  H                          z                                                                    ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                                                      j                            -                                                          1                              /                              2                                                                                ,                          k                                                n                                                                                    Δ                      ⁢                                                                                          ⁢                      y                                                        -                                                                                    H                        y                                            ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                                                      k                            +                                                          1                              /                              2                                                                                                      n                                            ⁢                                              -                                                  H                          y                                                                    ⁢                                              |                                                                              i                            +                                                          1                              /                              2                                                                                ,                          j                          ,                                                      k                            -                                                          1                              /                              2                                                                                                      n                                                                                    Δ                      ⁢                                                                                          ⁢                      z                                                                      )                                      +                          E              0                                ⁢                      |                                          i                +                                  1                  /                  2                                            ,              j              ,              k                                ⁢                      sin            ⁡                          (                                                ω                  ⁢                                                                          ⁢                  t                                +                ϕ                            )                                                          (        3        )            where E0 is an amplitude of the electric field of the incident wave in the wave source, ω is an angular frequency of the incident wave, φ is an initial phase of the incident wave in the wave source and the amplitude E0 of the electric field of the incident wave is a function of coordinates.
In this Formula (3), a value obtained by adding an electric field component when light propagation from the outside of the wave source is calculated to an electric field component vibrating as the incident wave is used. For this reason, light propagation is calculated even in the wave source, and therefore reflection is not produced.
FIG. 2 shows a simulation example with consideration given to light propagation in the wave source.
The same model used in FIG. 1 is used here, too.
Because there is no more reflection by the wave source 1, the simulation result shown in this FIG. 2 shows arc-shaped stripe patterns between the wave source 1 and reflecting surface 2 produced by one-time interference between light propagating from the wave source 1 toward the reflecting surface 2 and reflected light propagating from the reflecting surface 2 toward the wave source 1.
The wave source in which reflection is produced by subjecting the current source to forced vibration as shown in Formula (a) is called a “hard source”, while the wave source in which a propagation term is added to vibration of the incident wave as shown in Formula (3) is called a “soft source”. Soft source is generally used in optical analyses.
However, in the case of the wave source set using the soft source in Formula (3), the amplitude of the incident wave which is expected as a precondition for the simulation is not correctly reflected in simulation results, which poses a problem that intensity of incident light cannot be set correctly.
FIG. 3 shows an example of a simulation for confirming intensity of incident light and FIG. 4 shows another example of a simulation for confirming intensity of incident light.
In FIG. 3, electric field vibration of light propagating through a medium having a refractive index of 1.5 is simulated when the electric field of an incident wave of the wave source is subjected to vibration using a sine wave having an amplitude of 1 V/m.
As calculation conditions, a first condition under which the size of grids in the light propagation direction is set to 10 nm and time step is set to 13.343 as and a second condition under which the size of grids is set to 20 nm and time step is set to 18.792 as are used. FIG. 3 shows simulation results under the respective calculation conditions. According to the simulation results shown here, though the amplitude of the wave source and the physical analysis model are invariable, the amplitude varies depending on the difference in the calculation conditions. Moreover, none of the electric field amplitudes obtained from the simulation results matches the amplitude of 1 V/m which should originally be obtained.
In FIG. 4, a Gaussian pulse having a pulse width of 16.7 ns with the electric field of an incident wave having a peak electric field of 1 V/m is set and electric field vibration of propagating light is simulated for each of four different types of refractive index of the wave source. Note that the grid size and space step are commonly set to 10 nm and 10 as respectively for all the four types of refractive indices.
In the simulation result shown in this FIG. 4 as in the case of the sine wave shown in FIG. 3, the amplitude of the propagating electric field vibration varies depending on the refractive index though the setting of the electric field of the wave source is constant.